Behavior of Gases: Finding the Molar Mass of a Fictitious
Gas Using Temperature and Average Velocity
OBJECTIVES
• Determine the molar mass of a fictitious gas in a simulation
• Learn the relationship between temperature and kinetic energy
INTRODUCTION
The molecules of matter at ordinary temperatures can be considered to be in ceaseless,
random motion at high speeds. The average translational kinetic energy for these molecules
can be deduced from the Boltzmann distribution. Knowing the velocity and the temperature of
these molecules at different temperatures will allow us to calculate a value for the Molar Mass.
The Boltzmann distribution of energies can be broken down to relate average velocities to
temperature using the following relation:
3
1
kT = mv 2
2
2
k = 1.38 x 10-23 J/K
T in Kelvin
m of a single particle in kg
v in m/s
We can eliminate the 1/2 factor by multiplying both sides by 2 giving us:
3kT = mv 2
y = mx + b
You can see how this equation can be viewed and plotted as a linear relationship with v2 as the
x-axis and 3kT as the y-axis.
PROCEDURE
A. Go to the University of Colorado website for science simulations: phet.colorado.edu.
1. Click on the “Play with Simulation” button.
2. Click on “Chemistry”
3. Find the lab the says “Gas Properties” and click on it.
4. You can either use the simulation online or download it as a .jar (Java archive) file. If you
click to play and you get a blank screen, you will need to download it.
5. Open the .jar file and run it. If you need to install Java on your computer you can do so
here https://java.com/en/download/manual.jsp. You may need to restart your computer
after installing.
B. SETTING UP THE EXPERIMENT
1. Click on “Constant Volume”
2. Click on “Measurement Tools”, then select “Species Information”
3. Click on “Advanced Options” and deselect “Molecules Collide”
4. Record your data from the experiment in the table below for Temperature, Pressure, and
Average Speed
Heavy Species
T(K)
Pressure (atm)
Average Speed (m/s)
Light Species
T(K)
Pressure (atm)
Average Speed (m/s)
C. RUNNING THE EXPERIMENT
1. Use the pump handle to pump in between 300 and 600 particles
2. Record the values for the Temperature, Pressure, and Average Speed
3. Use the Heat Control to raise or lower the temperature and record at least 4 additional
data points with a total temperature range of at least 500K between the lowest and
highest temperatures and at least two below room temperature (300K)
4. Once you are finished recording your data points, click on the “Reset” button to begin a
new experiment. (You may need to close the Measurement Tools to find the reset
button).
5. Choose the “Light Species” for the Gas in Pump, and repeat steps 1 – 4. Be sure to
choose at least one temperature in this series of measurements that is the same as the
first series
D. DATA ANALYSIS
1. Plot your data as explained in the Introduction for your heavy species and attach to your
report.
2. Find the mass of a single particle in kg, and the mass of one mole of particles in g/mol.
Show your calculations below. (Note: You will need to find the slope of your line. To find
the slope of your line to more than one significant figure in Excel you may need to use
the SLOPE function. In a cell type =SLOPE(range of y-values),(range of x-values))
3. Repeat your analysis for the light species.
E. QUESTIONS
1. What is the relationship between temperature and average velocity?
2. Using the two measurements that were at the same temperature for the two species,
how did the average velocity compare between the heavy and light particles? Explain
why this is.
3. How did the pressure respond to the changes in temperature? Explain the reason for
this
Research Extension
Gas Pressure and Temperature Relationships Simulation
A. QUALITATIVE DATA
1. What do you expect to happen to the pressure of a gas when a sealed system heats up?
Cools down? What evidence in your everyday life supports your statements?
B. SETTING UP THE EXPERIMENT
1. Click on “Constant Volume”
2. Click on “Measurement Tools”, then select “Species Information”
3. Click on “Advanced Options” and deselect “Molecules Collide”
4. Chose the “Light Species”
5. Record your data from the experiment in the table below for Temperature, Pressure, and
number of particles.
6. Reset the experiment if needed.
Light Species
T(K)
Pressure (atm)
Number of Particles
Light Species
T(K)
Pressure (atm)
Number of Particles
Name:_______________________
Date:_____________________
Partners__________________________________________________________
Light Species
T(K)
Pressure (atm)
Number of Particles
C. RUNNING THE EXPERIMENT
1. Use the pump handle to pump in between 500 and 600 particles
2. Set the temperature to ~500°C (773K)
3. Record the values for the Temperature, Pressure, and number of particles.
4. Use the Heat Control to lower the temperature by about 100° and record the
temperature and pressure.
5. Continue recording temperature and pressure data, lowering the temperature by about
100° for each set of data. Keep changing temperature until you reach ~0°C (273K)
6. Once you are finished recording your data points, click on the “Reset” button to begin a
new experiment. (You may need to close the Measurement Tools to find the reset
button).
7. Repeat steps 1-5 two more times using between 300-400 particles and 100-200 particles
for the two runs.
D. DATA ANALYSIS
1. Graph your 3 data sets in a spreadsheet. What patterns do you see in your data? What
are the algebraic expressions that describes your patterns? Are there any similarities in
the graphs?
Name:_______________________
Date:_____________________
Partners__________________________________________________________
2. Did the number of particles affect the value of absolute zero from your data? Explain.
3. Describe the historical set up used to determine the value of absolute zero for the first
time.